International Journal of Theoretical Physics

, Volume 57, Issue 7, pp 2218–2232 | Cite as

Modulational Instability and Quantum Discrete Breather States of Cold Bosonic Atoms in a Zig-Zag Optical Lattice

  • Xia Chang
  • Jiayu Xie
  • Tianle Wu
  • Bing Tang


A theoretical study on modulational instability and quantum discrete breather states in a system of cold bosonic atoms in zig-zag optical lattices is presented in this work. The time-dependent Hartree approximation is employed to deal with the multiple body problem. By means of a linear stability analysis, we analytically study the modulational instability, and estimate existence conditions of the bright stationary localized solutions for different values of the second-neighbor hopping constant. On the other hand, we get analytical bright stationary localized solutions, and analyze the influence of the second-neighbor hopping on their existence conditions. The predictions of the modulational instability analysis are shown to be reliable. Using these stationary localized single-boson wave functions, the quantum breather states corresponding to the system with different types of nonlinearities are constructed.


Zig-zag optical lattices Cold bosonic atoms Modulational instability Quantum breather states 



Acknowledgments This work was supported by the National Natural Science Foundation of China under Grant No. 11604121, the Scientific Research Fund of Hunan Provincial Education Department under Grant No. 16B210, the Natural Science Fund Project of Hunan Province under Grant No. 2017JJ3255, and the Natural Science Fund Project of Jishou University under Grant No. jdx17036.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Physics, Mechanical and Electrical EngineeringJishou UniversityJishouChina

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